New answers tagged boundary-conditions
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First, I think that we should write the problem as
$$-\nabla(\varepsilon \nabla \phi) = \rho + \sigma\, .$$
Then, the weak form would be
$$\int\limits_\Omega \varepsilon \nabla \phi \nabla w d\Omega
- \int\limits_{\partial\Omega} \varepsilon w\nabla\phi\cdot\hat{n}d\Gamma
= \int\limits_\Omega f w d\Omega\, .$$
As you mentioned, the second term vanishes for ...
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